Suppose I have a graph with a set of edge, and a weight assigned to each edge. How can I find a maximum-weight matching of the edges? I think this is a classic CO problem but I don't know the name of the algorithm. I need this algorithm to solve an online programming puzzle.
Many books on operations research have material about matchings and weighted matchings, often only for the bipartite graph case. However, a book that treats both the general and bipartite case is Dieter Jungnickel, Graphs, Networks and Algorithms, Springer, 1999, Chapters 12 and 13.